Subject-specific estimation of central aortic blood pressure via system identification: preliminary in-human experimental study

Abstract

This paper demonstrates preliminary in-human validity of a novel subject-specific approach to estimation of central aortic blood pressure (CABP) from peripheral circulatory waveforms. In this “Individualized Transfer Function” (ITF) approach, CABP is estimated in two steps. First, the circulatory dynamics of the cardiovascular system are determined via model-based system identification, in which an arterial tree model is characterized based on the circulatory waveform signals measured at the body’s extremity locations. Second, CABP waveform is estimated by de-convolving peripheral circulatory waveforms from the arterial tree model. The validity of the ITF approach was demonstrated using experimental data collected from 13 cardiac surgery patients. Compared with the invasive peripheral blood pressure (BP) measurements, the ITF approach yielded significant reduction in errors associated with the estimation of CABP, including 1.9–2.6 mmHg (34–42 %) reduction in BP waveform errors (p < 0.05) as well as 5.8–9.1 mmHg (67–76 %) and 6.0–9.7 mmHg (78–85 %) reductions in systolic and pulse pressure (SP and PP) errors (p < 0.05). It also showed modest but significant improvement over the generalized transfer function approach, including 0.1 mmHg (2.6 %) reduction in BP waveform errors as well as 0.7 (20 %) and 5.0 mmHg (75 %) reductions in SP and PP errors (p < 0.05).

Appendix: ITF system identification procedure

Using the expressions for G _R (s) and G _F (s) in (1), (2) can be re-written as follows:

$$\frac{{\left( {s + \eta_{1R} } \right)e^{{\tau_{R} s}} + \eta_{2R} e^{{ - \tau_{R} s}} }}{{s + \eta_{1R} + \eta_{2R} }}P_{R} \left( s \right) = \frac{{\left( {s + \eta_{1F} } \right)e^{{\tau_{F} s}} + \eta_{2F} e^{{ - \tau_{F} s}} }}{{s + \eta_{1F} + \eta_{2F} }}P_{F} \left( s \right)$$

(15)

This relationship between two peripheral BP waveforms results in the following cost function for system identification via optimization:

$$J\, =\left\|{ \,\frac{{\left( {s + \eta_{1R} } \right)e^{{\tau_{R} s}} + \eta_{2R} e^{{ - \tau_{R} s}} }}{{s + \eta_{1R} + \eta_{2R} }}P_{R} \left( s \right) - \frac{{\left( {s + \eta_{1F} } \right)e^{{\tau_{F} s}} + \eta_{2F} e^{{ - \tau_{F} s}} }}{{s + \eta_{1F} + \eta_{2F} }}P_{F} \left( s \right)}\right\|_{2}$$

(16)

which can be minimized over the set of unknowns given by:

$$\varTheta = \left\{ {\tau_{R} , \eta_{1R} , \eta_{2R} , \tau_{F} , \eta_{1F} , \eta_{2F} } \right\}$$

(17)

which yields (3).

In solving (3), constraints can be incorporated into the system identification procedure. First, noting that end-diastolic trough is the most robust in the BP waveform against morphological distortion caused by wave reflection (i.e., the effect of reflected wave is small in early systole), the difference between τ _R and τ _F can be approximated by the trough-to-trough time delay between upper-body and lower-body BP measurements:

$$\tau_{d} = \tau_{F} - \tau_{R} ,$$

(18)

where τ _d is the “differential” time delay. Second, noting that all the parameters in the parallel tube-load model retain physical implications and thus must assume positive values, the following constraints hold:

$$\tau_{R} > 0, \quad \eta_{1R} > 0, \quad \eta_{2R} > 0, \quad \tau_{F} > 0, \quad \eta_{1F} > 0, \quad \eta_{2F} > 0$$

(19)

Furthermore, scrutinizing the expressions for η ₁ and η ₂ reveals the following:

$$\eta_{1} = \eta_{2} + \frac{1}{{R_{T} C_{T} }} < \eta_{2} + \frac{1}{{Z_{C} C_{T} }} = 3\eta_{2}$$

(20)

which yields the following constraints on the relative magnitudes of η _1R versus η _2R and η _1F versus η _2F :

$$\eta_{2R} < \eta_{1R} < 3\eta_{2R} , \quad \eta_{2F} < \eta_{1F} < 3\eta_{2F} .$$

(21)